Question

describe the benefits of writing a quadratic equation in vertex form and standard form. Name specific methods you can use while working with one form or the other

Answer 1

Vertex form let's you know where the vertex is. Since the vertex is the highest or lowest point, its going to tell you where the highest or lower point lyes.
Standard form of a parabola can be very useful for analyzing parabolas. So pretty much you can understand what each value is being used for.